AP Statistics Cumulative AP Exam Study Guide

Introduction to Statistics

• Statistics: Science of collecting, analyzing, and drawing conclusions from data.
• Descriptive Statistics: Methods of organizing and summarizing statistics.
• Inferential Statistics: Making generalizations from a sample to the population.

Key Concepts

• Population: An entire collection of individuals or objects.
• Sample: A subset of the population selected for study.
• Variable: Characteristic whose value changes.
• Data: Observations on single or multi-variables.

Types of Variables

• Categorical (Qualitative): Basic characteristics.
• Numerical (Quantitative): Measurements or observations of numerical data.
  • Discrete: Listable sets (counts).
  • Continuous: Any value over an interval of values (measurements).

Types of Data

• Univariate: One variable.
• Bivariate: Two variables.
• Multivariate: Many variables.

Distributions

• Symmetrical: Data on both sides are fairly the same shape and size.
• Bell Curve
• Uniform: Every class has equal frequency.
• Skewed: One tail longer than the other; skew direction indicated by tail direction.
• Bimodal: Two or more classes have large frequencies separated by another class.

Describing Numerical Graphs - S.O.C.S.

• Shape: Symmetrical, skewed, uniform, bimodal.
• Outliers: Gaps, clusters, etc.
• Center: Middle of the data (mean, median, mode).
• Spread: Variability (range, standard deviation, IQR).

Measures of Center

• Median: Middle point (50th percentile) of ordered data.
• Mean ((\mu)): Population parameter.
• x̄: Sample statistic.
• Mode: Most occurring data point.

Measures of Spread

• Range: Difference between max and min.
• IQR: Interquartile range (Q3 - Q1).
• Standard Deviation ((\sigma)): Typical deviation from the mean.
• Variance: Standard deviation squared.

Resistance to Outliers

• Resistant: Median, IQR.
• Non-Resistant: Mean, range, variance, standard deviation.

Correlation and Regression

• Correlation Coefficient (r): Strength and direction of a linear relationship.
• Least Squares Regression Line (LSRL): Line of best fit for bivariate data.
• Coefficient of Determination (r²): Proportion of variation in y explained by the relationship with x.

Probability

• Sample Space: Collection of all outcomes.
• Event: Sample of outcomes.
• Complement, Union, Intersection: Basic probability operations.
• Mutually Exclusive, Independent Events.
• Empirical Rule (68-95-99.7): For normal distributions.

Sampling Methods

• SRS (Simple Random Sample): Equal chance for each unit.
• Stratified: Divide into strata, then SRS each.
• Systematic: Systematic approach after random start.
• Cluster: Random location, sample all there.

Experimental Design

• Observational Study: Observes outcomes without treatment.
• Experiment: Imposes treatment on subjects.
• Control Group, Placebo, Blinding.
• Randomization, Blocking, Confounding Variables.

Random Variables and Distributions

• Discrete and Continuous.
• Binomial, Geometric Distributions.
• Normal Distributions.

Sampling Distribution

• Central Limit Theorem: Sampling distribution is normal if n > 30.

Confidence Intervals and Hypothesis Testing

• Confidence Intervals: Estimate unknown population parameter.
• Margin of Error: Precision of estimate.
• Hypothesis Testing: Determines if observed results are statistically significant.
• Type I and II Errors, Power of a Test.

Chi-Square Tests

• Goodness of Fit, Independence, Homogeneity.

These notes provide a comprehensive overview of the key concepts necessary for understanding and succeeding in AP Statistics, focusing on descriptive and inferential statistics, probability, experimental design, and more.